This invention relates to analogue computers. Various forms of analogue computers, particularly for solving differential equations, are well known. However, the automatic solving of non-differential polynominal equations can also be very useful.
For example, it is often necessary to discover the mass flow rate of a gas flowing in a pipe. For this purpose it is necessary to know not only the volume flow rate of the gas but also the density of the gas. The volume flow rate can readily be measured by known means. However, to discover the density of the gas, it is necessary to measure other parameters.
According to Boyles Law, for an ideal gas, P .alpha. Td, where d is the density P is the absolute pressure and T is the absolute temperature. Real gases deviate from this ideal, but their equations can usually be expressed in the general form; EQU P = f (d,T)
by using a digital computer suitably programmed to fit curves to measured sets of data over a required range on various well known gases, it can be demonstrated that these gases all closely fit an equation of the form: EQU P = .+-. Ad .+-. Bd.sup.2 .+-. Cd.sup.3 .+-. DdT .+-. Ed.sup.2 T .+-. Fd.sup.3 T 1
this equation is transposed to become EQU 0 = - P .+-. Ad .+-. Bd.sup.2 .+-. Cd.sup.3 .+-. DdT .+-. Ed.sup.2 T .+-. Fd.sup.3 T 2
a, b, c, d, e, and F represent positive constants. The values of these constant co-efficients may be ascertained for any particular gas by the above mentioned curve fitting process. The RHS of equation (2) for a particular gas is referred to hereinafter as the polynominal expression of the equation of the gas.
In order to discover the density of a gas, the pressure and temperature of the gas may be measured by known means and the equation (1) above solved for density d. Clearly, it would be most useful to obtain density d automatically from the measured parameters, temperature T and Pressure P.
More generally, it may often be useful to solve automatically non-differential polynominal equations in which only the variable for which a solution is required is raised to an integral power other than unity. Equations of this type may be expressed generally as follows: EQU 0 = A+Bx + Cx.sup.2 +Dx.sup.3 + . . . +Zx.sup.1 + A'a+B'ax + C'ax.sup.2 + D' ax.sup.3 + . . . +Z'ax.sup.m + A'A"b+b"bx + C"bx.sup.2 + C"bx.sup.3 + . . . +Z"bx.sup.n + . . .
where A, B, C, D, . . . Z, A', B', . . . etc. are constants, x is the variable for which a solution is required, a, b, . . . are known variables and l, m, n . . . are positive integral powers. Equations of this type (referred to hereinafter as polynominal equations of the type described) may contain only a single variable, being the unknown variable x, or any number of variables x, a, b, c . . . .